🧮 algebra

1. **Problem Statement:** Write the equation of a line in standard form that has x-intercept $(P,0)$ and y-intercept $(0,R)$. 2. **Recall the intercept form of a line:** The equati

1. **State the problem:** We have the old route equation $$y = \frac{2}{5}x - 4$$ and want the equation of a new route parallel to it passing through point $ (Q, P) $. 2. **Recall

1. **State the problem:** We are given two line segments AB and CD lying on lines with equations $2x - 4y = 8$ and $4x + 2y = 8$ respectively. We need to determine the relationship

1. **State the problem:** We need to find the equation of a line perpendicular to line AB that passes through the point (7, 6). 2. **Find the slope of line AB:** The line AB passes

1. **State the problem:** We have parallelogram WXYZ with side WX having equation $$y=\frac{1}{4}x - 6$$. We need to find the equation of segment YZ, which passes through point $(-

1. **State the problem:** We need to find how many contemporary DVD titles Jarred has given the system of equations: $$x + y = 3500$$

1. **State the problem:** Solve the system of linear equations: $$3a + 6b = 45$$

1. The problem is to simplify the expression $\frac{210io4iy4u21iuo31 - aby}{33}$.\n\n2. First, identify the terms: $210io4iy4u21iuo31$ and $aby$ appear to be non-numeric or symbol

1. The problem is to understand what happened to the term $28x$ in an expression or equation. 2. Often, terms like $28x$ can be combined, factored out, or canceled depending on the

1. **State the problem:** Simplify or factor the quadratic expression $4x^2 + 28x + 49$. 2. **Recall the formula:** To factor a quadratic expression of the form $ax^2 + bx + c$, we

1. Masalah: Tukar bentuk surd dari $\frac{\sqrt{3}}{2}$ kepada $\frac{\sqrt{2}}{2}$ seperti yang diminta. 2. Formula dan peraturan penting: Surd adalah bentuk akar yang tidak boleh

1. The problem is to simplify the expression surd 2 divided by 2 tau, which can be written as $\frac{\sqrt{2}}{2\tau}$. 2. Recall that $\tau$ is a constant equal to $2\pi$. So the

1. **State the problem:** Simplify the expression $$2x \cdot \frac{(x+y)(x-y)+2y^2}{2y(x-y)} \div \frac{x^2+y^2}{xy-y^2}$$. 2. **Rewrite the division as multiplication by the recip

1. Het probleem: Los de vergelijking $3x + 5 = 20$ op. 2. Formule en regels: Om een lineaire vergelijking op te lossen, isoleren we de variabele $x$ door beide zijden van de vergel

1. **Stating the problem:** Risolvi l'equazione $$5x + 2(x+1) - 3x = 4x - 3 + x$$. 2. **Formula and rules:** Per risolvere equazioni lineari, si applica la proprietà distributiva,

1. Il problema chiede di risolvere un'equazione, ma non è stata fornita un'equazione specifica. 2. Per risolvere un'equazione, si applicano regole di algebra come isolare la variab

1. **State the problem:** Solve the equation $$\frac{52}{x+30} - \frac{52}{x} = \frac{27}{10}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, find a co

1. **State the problem:** We want to find the number of TV sets $x$ to produce and sell per week to maximize the weekly profit, given the cost function and selling price.

1. **State the problem:** Find two positive numbers whose sum is 300 and whose product is maximum. 2. **Set variables:** Let the two numbers be $x$ and $y$.

1. **Problem statement:** Simplify the algebraic expressions for waagerecht (horizontal) A and B. 2. **Formula and rules:** Combine like terms by adding or subtracting coefficients

1. **State the problem:** We need to find a two-digit number whose digits sum to 12 and when reversed, the new number is \(\frac{4}{7}\) of the original number. 2. **Define variabl